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IEE 475: Simulating Stochastic Systems

Theodore P. Pavlic

Archived lectures from undergraduate course on stochastic simulation given at Arizona State University by Ted Pavlic

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IEE 475: Lecture I (2025-10-30): Statistical Reflections

IEE 475: Simulating Stochastic Systems ·

2025/10/30

In this lecture, we review statistical fundamentals – such as the origins of the t-test, the meaning of type-I and type-II error (and alternative terminology for both, such as false positive rate and false negative rate) and the connection to statistical power (sensitivity). We review the Receiver Operating Characteristic (ROC) curve and give a qualitative description of where it gets its shape in a hypothesis test. We close with a validation example (from Lecture H) where we use a power analysis on

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Lecture H (2025-10-28): Verification, Validation, and...

IEE 475: Simulating Stochastic Systems ·

2025/10/29

At the start of this lecture, we review statistical topics and fitting techniques from Unit G (particularly Lecture G3, on goodness of fit). In particular, we review hypothesis testing fundamentals (type-I error, type-II error, statistical power, sensitivity, false positive rate, true negative rate, receiver operating characteristic, ROC, alpha, beta) and then go into examples of using Chi-squared and Kolmogorov–Smirnov tests for goodness of fit for arbitrary distributions. We also introduce

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Lecture G3 (2025-10-23) Input Modeling, Part 3...

IEE 475: Simulating Stochastic Systems ·

2025/10/23

In this lecture, we (nearly) finish our coverage of Input Modeling, where the focus of this lecture is on parameter estimation and assessing goodness of fit. We review input modeling in general and then briefly review fundamentals of hypothesis testing. We discuss type-I error, p-values, type-II error, effect sizes, and statistical power. We discuss the dangers of using p-values at very large sample sizes (where small p-values are not meaningful) and at very small sample sizes (where large p-values

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IEE 475: Lecture G2 (2025-10-21): Input Modeling,...

IEE 475: Simulating Stochastic Systems ·

2025/10/22

In this lecture, we continue discussing the choice of input models in stochastic simulation. Here, we pivot from talking about data collection to selection of the broad family of probabilistic distributions that may be a good fit for data. We start with an example where a histogram leads us to introduce additional input models into a flow chart. The rest of the lecture is about choosing models based on physical intuition and the shape of the sampled data (e.g., the shape of histograms). We close

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Lecture G1 (2025-10-16): Input Modeling, Part 1 (Data...

IEE 475: Simulating Stochastic Systems ·

2025/10/16

In this lecture, we introduce the detailed process of input modeling. Input models are probabilistic models that introduce variation in simulation models of systems. Those input models must be chosen to match statistical distributions in data. Over this unit, we cover collection of data for this process, choice of probabilistic families to fit to these data, and then optimized parameter choice within those families and evaluation of fit with goodness of fit. In this lecture, we discuss issues

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Lecture F (2025-10-02): Midterm Review for IEE 475...

IEE 475: Simulating Stochastic Systems ·

2025/10/03

During this lecture, we review the topics covered up to this point in the course as preparation for the upcoming midterm exam. Students are encouraged to bring their own questions to class so that we can focus on the topics that students feel like they need the most help with.

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Lecture E2 (2025-09-30): Random-Variate Generation

IEE 475: Simulating Stochastic Systems ·

2025/10/01

In this lecture, we review pseudo-random number generation and then introduce random-variate generation by way of inverse-transform sampling. In particular, we start with a review of the two most important properties of a pseudo-random number generator (PRNG), uniformity and independence, and discuss statistically rigorous methods for testing for these two properties. For uniformity, we focus on a Chi-square/Chi-squared test for larger numbers of samples and a Kolmogorov–Smirnov (KS) test for

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Lecture E1 (2025-09-25): Random-Number Generation

IEE 475: Simulating Stochastic Systems ·

2025/09/25

In this lecture, we first cover some discrete distributions (and the Poisson process) that we ran out of time for during the previous lecture. We then launch into a discussion of how to generate pseudo-random numbers distributed uniformly between 0 and 1 (which are necessary for us to easily generate random variates of any distribution). We talk about the two most important properties of a pseudo-random number generator (PRNG), uniformity and independence. We then talk about desirable properties

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Lecture D2 (2025-09-23): Probabilistic Models

IEE 475: Simulating Stochastic Systems ·

2025/09/23

In this lecture, we review basic probability fundamentals (measure spaces, probability measures, random variables, probability density functions, probability mass functions, cumulative distribution functions, moments, mean/expected value/center of mass, standard deviation, variance), and then we start to build a vocabulary of different probabilistic models that are used in different modeling contexts. These include uniform, triangular, normal, exponential, Erlang-k, Weibull, and Poisson variables

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Lecture D1 (2025-09-18): Probability and Random...

IEE 475: Simulating Stochastic Systems ·

2025/09/18

In this lecture, we introduce the measure-theoretic concept of a random variable (which is neither random nor a variable) and related terms, such as outcomes, events, probability measures, moments, means, etc. Throughout the lecture, we use the metaphor of probability as mass (and thus probability density as mass density, and a mean as a center of mass). This allows us to discuss the "statistical leverage" of outliers in a distribution (i.e., although they happen infrequently, they still have the

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Lecture C2 (2025-09-16): Beyond DES Simulation – SDM,...

IEE 475: Simulating Stochastic Systems ·

2025/09/16

This lecture provides some historical background and motivation for System Dynamics Modeling (SDM) and Agent-Based Modeling (ABM), two other simulation modeling approaches that contrast with Discrete Event System (DES) simulation.In particular, in this lecture, we briefly introduce System Dynamics Modeling (SDM) and Agent-Based/Individual-Based Modeling (ABM/IBM) as the two ends of the simulation modeling spectrum (from low resolution to high resolution). The introduction of ABM describes

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Lecture C1 (2025-09-11): Basic Simulation Tools and...

IEE 475: Simulating Stochastic Systems ·

2025/09/11

This lecture covers content related to implementing simulations with spreadsheets and the motivations for the use of special-purpose Discrete Event System Simulation tools. In particular, we discuss different approaches to implementing Discrete Event System (DES) simulations (DESS) with simple spreadsheets (e.g., Microsoft Excel, Google Sheets, Apple Numbers, etc.). We cover inventory management problems (such as the newsvendor model) as well as Monte Carlo sampling and stochastic activity networks

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Lecture B3 (2025-09-09): DES Examples, Part II (and...

IEE 475: Simulating Stochastic Systems ·

2025/09/09

In this lecture, we close out our review of DES fundamentals and hand simulation. After going through a hand-simulation example one last time, we show how to implement a Discrete Event System (DES) simulation using a spreadsheet tool like Microsoft Excel without any "macros" (VBA, etc.). This involves defining relationships ACROSS TIME that allow the spreadsheet to (in a declarative fashion) reconstruct the trajectory that is the output of the simulation.At the end of the lecture, we pivot to

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Lecture B2 (2025-09-04): DES Examples, Part I

IEE 475: Simulating Stochastic Systems ·

2025/09/04

In this lecture, we review fundamentals of Discrete Event System (DES) simulation (e.g., entities, resources, activities, processes, delays, attributes) and we run through a number of DES modeling examples. These examples show how different research/operations questions can lead to different choices of entities/resources/etc. We close with a hand-simulation example of a single-channel, single-server queue with provided interarrival times and service times.

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Lecture B1 (2025-09-02): Fundamental Concepts of...

IEE 475: Simulating Stochastic Systems ·

2025/09/02

In this lecture, we cover fundamentals of discrete-event system (DES) simulation (DESS). This involves reviewing basic simulation concepts (entities, resources, attributes, events, activities, delays) and introducing the event-scheduling world view, which provides a causality framework on which an automatic simulation of a DES system can be built. We also discuss briefly how the stochastic modeling inherent to DESS means that outputs will be variable and thus will require rigorous statistics to make

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Lecture A2 (2025-08-28): Introduction to Simulation...

IEE 475: Simulating Stochastic Systems ·

2025/08/28

In this lecture, we introduce the three different simulation methodologies (agent-based modeling, system dynamics modeling, and discrete event system simulation) and then focus on how stochastic modeling is used within discrete-event system simulation. In particular, we define terms such as system, dynamic system, state, state variable, activity, delay, resource, entity, and the notion of "input modeling."

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Lecture A1 (2025-08-26): Introduction to Modeling

IEE 475: Simulating Stochastic Systems ·

2025/08/26

In this lecture, we introduce Industrial and Systems Engineering as a blend of science and engineering that necessitates model building. We then define model (as something that answers a "What If" question) and different types of models. This gives us an opportunity to discuss how modeling is less about describing reality and more about generating tools to do useful things/make useful predictions. We end with a comparison of mental and quantitative models, as well as a comparison of different types

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Lecture 0 (2025-08-21): Course Introduction

IEE 475: Simulating Stochastic Systems ·

2025/08/21

This lecture introduces students to IEE 475 (Simulating Stochastic Systems), a required course for Industrial Engineering majors that covers the design and analysis of simulation models of real-world engineered systems. The lecture covers contents of the syllabus as well as where students can find more information in the Canvas Learning Management System site for the course.

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Lecture M (2024-12-03): Final Exam Review

IEE 475: Simulating Stochastic Systems ·

2024/12/04

In this lecture, we prepare for the final exam and give a brief review of all topics from the course. Students are encouraged to bring their own questions so that the focus of the class is on the topics that students feel they need the most help with.

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Lecture L (2024-11-26) Course Wrap-Up

IEE 475: Simulating Stochastic Systems ·

2024/11/27

In this lecture, we wrap up the course content in IEE 475. We first do a quick overview of the four variance reduction techniques (VRT's) covered inUnit K. That is, we cover: common random numbers (CRN's), antithetic variates (AV's), importance sampling, and control variates. We then remember some general comments about the goal of modeling and commonalities seen across simulation platforms (as well as the different types of simulation platforms in general).

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IEE 475: Simulating Stochastic Systems

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